Magnetic Resonance Image Processing Using Levy Distributed Anisotropic Diffusion

We consider the physical nature of the self-diffusion of water molecules in tissue and explore how (Nuclear) Magnetic Resonance (MR) imaging may be used as a means of measuring the rate of diffusion in vivo. A discussion is presented on how these techniques may be implemented as a non-invasive means of assessing the response of tumours to novel therapeutics including some of the basic advantages and disadvantages when compared to other methods. The physical basis and mathematical models for diffusion are considered together with models for the distribution of the diffusion co-efficient including a Levy distributed model. Using a Levy distributed diffusion model, we develop a novel algorithm for the purpose of improving the signal-to-noise ratio of MR images.